The reason to post the other post about the KKp is that i was having a conversation with a friend about it. Turns out he is a supporter of it. I think it is rather obvious that it isnt true. I posted the argument about infinite beliefs already, but there is more to be said about it.

As it is, some years ago i spent some time discussing KKp with a friend (kennethamy, prof. emeritus, RIP). Unfortunately, i googled around and cudnt find the specific threads. It was on freeratio (FRDB) or what used to be call philosophy forums (now able2know). I found a couple of threads about it, but not exactly what i was looking for.

Im of the opinion that the best way to change wrong opinions in people is not to talk to them about it, and give arguments. This usually results in combative behavior (such are humans). Instead i recommend reading a lot about the subject. So, i looked for some writings to send to my friend about KKp. Here’s what i wrote to him on Skype:

[13:12:42] Emil – Deleet: sketch of proof
[13:12:42] Emil – Deleet:
[13:12:48] Emil – Deleet: and no
[13:12:49] Emil – Deleet: ofc not
[13:12:54] Emil – Deleet: and yes, it is obvious
[13:13:11] Emil – Deleet: i went and looked for my conversation with kennethamy about it
[13:13:16] Emil – Deleet: didnt find it
[13:13:21] Emil – Deleet: well “it”
[13:13:29] Emil – Deleet: since i have talked with him about it many times
[13:13:45] Emil – Deleet: (kennethamy is a now dead prof. emeritus that i knew)
[13:16:41] Emil – Deleet:
[13:16:50] Emil – Deleet: i think i read that art. years ago
[13:21:22] Emil – Deleet: not particularly clear regarding important things (suprise exam argument)
[13:23:06] Emil – Deleet: //
if u like infinite numbers of beliefs, u might like infinitism as a way out of the regression argument of epis.
[13:23:20] Emil – Deleet:
[13:23:37] Emil – Deleet: i read Klein’s papers in high school (by myself, was curious)
[13:23:41] Emil – Deleet: perhaps u will like them
[13:23:49] Emil – Deleet: i found them interesting but not convincing
[13:24:21] Emil – Deleet: if i had time to go into some depth about KKp again, id read
[13:24:33] Emil – Deleet: u might like that as well, as it is a defense of KKp
[13:30:50] Emil – Deleet: also useful
[13:30:50] Emil – Deleet:
[13:30:59] Emil – Deleet: contains some common counterexamples
[13:32:43] Emil – Deleet: Swartz’s remark also comes to mind “Over the years I have found that a great many claims in epistemology are refuted by looking at the actual beliefs of young children and uneducated and unsophisticated adults.”
[13:33:01] Emil – Deleet: cf.



(KK)If one knows that p, then one knows that one knows that p.

A0is the proposition that 1+1=2.
A1is the proposition that Emil knows that 1+1=2.
A2is the proposition that Emil knows that Emil knows that 1+1=2.

Anis the proposition that Emil knows that Emil knows that … that 1+1=2.
Where “…” is filled by “that Emil knows” repeated the number of times in the subscript of A.

1. Assumption for RAA
For any proposition, P, and any person, x, if x knows that P, then x knows that x knows that P.

2. Premise
Emil knows that A0.

3. Premise
There is a set, S1, such that A0belongs to S1, and A1belongs to S1, and … and Anbelongs to S1, and the cardinality of S1is infinite, and S1is identicla to SA.

4. Inference from (1), (2), and (3)
For any proposition, P, if P belongs to SA, then Emil knows that P.

5. Premise
It is not the case that, for any proposition, P, if P belongs to SA, then Emil knows that P.

6. Inference from (1-5), RAA
It is not the case that, for any proposition, P, and any person, x, if x knows that P, then x knows that x knows that P.

Proving it
Proving that it is valid formally is sort of difficult as it requires a system with set theory, predicate logic with quantification over propositions. The above sketch should be enough for whoever doubts the formal validity.

To my knowledge this has not been so extensively done, but it seems like an interesting line of evidence.

Here is a random sample i came across:

Lubinski, Webb, et al., 2001, Journal of Applied Psychology,
86, 718-729). A 10-Year Longitudinal Study of the Top 1 in 10,000
in mathematical or verbal reasoning (N = 320) identified in the
early 1980s (at age 13) [SMPY Cohort 3]. // found via Long-Term Effects of Educational Acceleration in A Nation Deceived: How Schools Hold Back America’s Brightest Students volume 2, p. 114.

M=225, F=59, total = 284, so some must be missing from the follow-up. I skimmed but didnt find the sex ratio about initial participants. But it seems unlikely that all the dropouts were women such that the data are completely bogus for estimating.

If there is a sex difference in mean ability, then this difference becoms progressivly larger as one goes further and further away from the mean of 100. This can be used to go backwards and estimate the sex difference. The ratio in the data above is 3.81:1, M:F.

Assuming that there is no difference between sexes in variation (in contrast to what was earlier believed), then one can calculate expected ratios:

Sex ratio Mean diff Men >180 Women >180 Men mean Women mean
9.0596324742 6 1.42E-007 1.57E-008 103 97
7.5396273569 5.5 1.30E-007 1.73E-008 102.75 97.25
6.2746501907 5 1.19E-007 1.90E-008 102.5 97.5
5.2219106584 4.5 1.09E-007 2.09E-008 102.25 97.75
4.3457994826 4 9.96E-008 2.29E-008 102 98
3.6166820496 3.5 9.11E-008 2.52E-008 101.75 98.25
3.0098949676 3 8.32E-008 2.77E-008 101.5 98.5
2.5049120246 2.5 7.60E-008 3.04E-008 101.25 98.75
2.0846535716 2 6.95E-008 3.33E-008 101 99
1.7349029347 1.5 6.34E-008 3.66E-008 100.75 99.25
3.7521222492 3.6 9.27E-008 2.47E-008 101.8 98.2
3.8925671421 3.7 9.44E-008 2.43E-008 101.85 98.15

I did it semi-manually using this site (my data is here), as i didnt want to go thru the trouble of finding the math way to solve it backwards. Thru iterating one can get pretty close, and the ratio is not that significant anyway with such a small sample set. But given the data, the sex mean difference is around 3.6-3.7. This number fits well with other studies (random example).

Edited to add: This sample was tested at age 13, thus before men have the ~4 IQ advantage per the developmental theory. But the data still fits. It wud be better if one cud find samples that are based on inclusion tests at a later age, say 20. Data from high-IQ societies may be distorted due to self-selection effects.

It began with this conversation with my friend Chad on Skype:


[09:54:34] Chad Stearns – Economist: A friend of mine met Aubrey De Grey
[09:54:41] Chad Stearns – Economist: And did some similar research.
[09:57:21] Emil – Deleet: de grey is pretty cool guy
[09:57:28] Emil – Deleet: autodidact ppl ftw
[11:14:06] Emil – Deleet: now i started reading wikipedia..
[11:14:07] Emil – Deleet: dam u
[11:14:19] Emil – Deleet: which reminded me that i need to read up on educational research
[11:14:27] Emil – Deleet: since the pirate party will need to have some opinions on education
[11:14:36] Emil – Deleet: i have some opinions, but need more data for specifics
[11:14:50] Chad Stearns – Economist: What kind of opinions?
[11:17:13] Emil – Deleet: 1) primary school teachers (PSTs) are currently of low quality
2) we can fix this by copying the finnish system; make PSTs education a university degree. this makes it more prestigious which attracts smarter ppl. and it increases the quality of the education.
3) girls do much better in school. perhaps we shud do something about this. for instance, splitting classes into active-hands-on classes, and listening and sit still classes.
[11:18:36] Emil – Deleet: 4) formal learning is not a very fast way of learning. some ppl want to learn on their own. we shud open up for this approach by removing bureaucratic rules that make it impossible, giving ppl credit for learning themselves.
[11:20:34] Emil – Deleet: 5) the most important two things for learning is intellectual ability (intelligence and memory), and motivation. the first we cannot do much about so easily. the second we can. due to the way the human mind works inre. gratification, gamification is a very good way to motivate ppl to learn.
consequrntly, we shud employ gamification in schools. this mixes well with (4).
examples are: khan academy, memrise, duolingo, but there are many more options open.
[11:22:09 | Edited 11:23:17] Emil – Deleet: 6) there needs to be a major overhaul of the topics taught in school. some things which are important to everyone are neglected, such as knowledge about statistics and probability. also critical thinking (and later, logic).
we can make space for these by getting rid of things that many ppl dont need to know, such as advanced trigonometry, interpretation of works of fiction.
need more focus on basic things in language classes, such as being able to write clearly, and writing a letter.
[11:23:25] Emil – Deleet: i perhaps forgot some things
[11:23:30] Emil – Deleet: but these are the basic things
[11:26:05] Emil – Deleet: 7) perhaps we shud not be using so much money on long university degrees. cf. academic inflation.
[11:26:13] Chad Stearns – Economist: I was just thinking the other day about how worthless the writing classes I have taken were.
[11:26:23] Chad Stearns – Economist: Honstly, 4chan has taught me how to write.
[11:26:31] Emil – Deleet: ^^
[11:26:38] Emil – Deleet: peer preassure to spell properly
[11:26:44] Emil – Deleet: or pressure
[11:26:47] Emil – Deleet: or preasure
[11:26:49] Emil – Deleet: who knows
[11:26:51] Emil – Deleet: english spelling -.-
[11:27:03] Chad Stearns – Economist: Having to regularly express page long ideas has taught me to communicate. Being forced to talk about an arbritrary topic in some horribly structured way does not teach me how to write.
[11:27:17] Chad Stearns – Economist: I have never heard of “preasure”
[11:27:30] Emil – Deleet: just as mispelling :P
[11:27:32] Emil – Deleet: as u wrote the other day
[11:27:42] Emil – Deleet: (funny since its itself a misspelling)
[11:28:38] Chad Stearns – Economist: I realized “slept” is not a word.
[11:28:46] Chad Stearns – Economist: Too bad reality, its a word now in my book.
[11:28:51] Emil – Deleet: it is
[11:29:12] Emil – Deleet:
[11:29:22] Emil – Deleet: one or two words
[11:29:25] Emil – Deleet: depending on how to count
[11:30:25 | Edited 11:30:51] Emil – Deleet: t.i.
to sleep, i sleep, i SLEPT = simple past tense
i have SLEPT = participle
[11:32:39] Emil – Deleet:
[11:32:42] Emil – Deleet: so many categories -.-
[11:46:32 | Edited 11:46:38] Emil – Deleet: 8) schools shud no longer give space to various religious indoctrination (which they do in Denmark).
[12:07:30] Emil – Deleet: 9) testing of Esperanto as a method of teaching foreign languages faster.
[12:08:16 | Edited 12:08:17] Emil – Deleet: 10) perhaps moving around classes. some mathematics concepts are difficult to teach to 6 year olds, but are easy to teach to 12 year olds. language is easier for smaller children. perhaps just postpone math teaching to later in school.



The reason to do the studying, as also mentioned above, is that the Pirate Party (Denmark) will need to have a broad political platform. I want to help form it to make sure that it is evidence-based, and not based on educational romanticism (see below).



Now i have finished the first round of research. Here are some stops on the journey:

Autodidacticism (also autodidactism) is self-directed learning that is related to but different from informal learning. In a sense, autodidacticism is “learning on your own” or “by yourself”, and an autodidact is a self-teacher. Autodidacticism is a contemplative, absorptive procession. Some autodidacts spend a great deal of time reviewing the resources of libraries and educational websites. One may become an autodidact at nearly any point in one’s life. While some may have been informed in a conventional manner in a particular field, they may choose to inform themselves in other, often unrelated areas.

Autodidactism is only one facet of learning, and is usually complemented by learning in formal and informal spaces: from classrooms to other social settings. Many autodidacts seek instruction and guidance from experts, friends, teachers, parents, siblings, and community. Inquiry into autodidacticism has implications for learning theory, educational research, educational philosophy, and educational psychology.


Wikipedia is heaven for autodidacts!

Gifted education (also known as Gifted and Talented Education (GATE), Talented and Gifted (TAG), or G/T) is a broad term for special practices, procedures and theories used in the education of children who have been identified as gifted or talented. There is no standard global definition of what a gifted student is.

In 2011, the National Association of Gifted Children published a position paper that defined what a gifted student is. Gifted describes individuals who demonstrate outstanding aptitude or competence in one or more domains. Aptitude is defined as an exceptional ability to learn or reason. Competence is defined as documented performance or achievement in the top 10% of the population.[1]


Very interesting area. Not only becus im a such student (and was in primary school as well, where i wasted time more or less). But becus the area has not been given much attention recently. The attention is usually on helping low-scoring students, especially those from weak SES backgrounds including immigrants (typically muslims in Denmark, in the US blacks and latinos).


On the page i found the very, very interesting paper/book:

I definitely recommend reading volume 1 of it, and perhaps volume 2 as well. I have not had time to read volume 2 yet, but i will i think.


Two other background readings on the subject:


and a very nice summary of the current policies about education, and how they are completely out of touch with reality, by Charles Murray of The Bell Curve fame (which i shud read as well). and his book length treatment of the same topic which i also want to read. Fairly decent reviews some of these are very cool

UnCollege is a social movement that aims to change the notion that going to college is the only path to success.[1][2][3] UnCollege was founded by Dale Stephens in 2010.[4][5]


According to the UnCollege website, the movement is founded on these principles:

  • Many people pay too much for university and learn too little.
  • You can get an amazing education anywhere—but you’ll have to stop writing papers and start doing things.
  • You need an excellent education to survive in a world where 50% of the population is under 30.
  • Subjects taught in traditional universities are often contrived, theoretical, and irrelevant, promoting conformity and regurgitation rather than innovation and learning.
  • You don’t have to decide what to do with your life at age 18.
  • You can contribute to society without necessarily having a university degree.
  • You cannot rely on university to give you a complete and relevant education when professors are often more interested in researching than teaching.
  • If you want to gain the skills requisite for success, you must hack your education.[20]

According to the UnCollege website, college, while not itself adverse, needs significant changes because:

  • Tuition is rising at twice the rate of inflation
  • Students are not learning
  • Students are incurring high levels of debt to finance their educations.


Parker attended Oakton High School in Fairfax County, Virginia for two years before transferring to Chantilly High School in 1996 for his junior and senior years.[11] While there, Parker wrote a letter to the school administration and persuaded them to count the time he spent coding in the computer lab as a foreign language class.[11] As a result, towards the end of Parker’s senior year at Chantilly, he was mostly writing code and starting companies.[11] He graduated in 1998. While still in high school, he interned for Mark Pincus (the current CEO of Zynga) at Pincus’s Washington D.C. startup FreeLoader.[12] He won the Virginia state computer science fair for developing a Web crawler, and was recruited by the C.I.A..[3] By his senior year of high school, Parker was earning more than $80,000 a year through various projects, enough to convince his parents to allow him to skip college and pursue a career as an entrepreneur.[3]




Some time ago i decided to look into nuclear power. While i havent had time yet to read some of the books i mentioned there, i read this paper. no paywall

Nuclear Energy and Health: And the Benefits of Low-Dose Radiation Hormesis


Energy needs worldwide are expected to increase for the foreseeable future, but fuel supplies are limited. Nuclear reactors could supply much of the energy demand in a safe, sustainable manner were it not for fear of potential releases of radioactivity. Such releases would likely deliver a low dose or dose rate of radiation, within the range of naturally occurring radiation, to which life is already accustomed. The key areas of concern are discussed. Studies of actual health effects, especially thyroid cancers, following exposures are assessed. Radiation hormesis is explained, pointing out that beneficial effects are expected following a low dose or dose rate because protective responses against stresses are stimulated. The notions that no amount of radiation is small enough to be harmless and that a nuclear accident could kill hundreds of thousands are challenged in light of experience: more than a century with radiation and six decades with reactors. If nuclear energy is to play a significant role in meeting future needs, regulatory authorities must examine the scientific evidence and communicate the real health effects of nuclear radiation. Negative images and implications of health risks derived by unscientific extrapolations of harmful effects of high doses must be dispelled.
Keywords: sustainable nuclear energy, radiation health effects, radiation hormesis, social acceptance, regulatory implications


I have had this on my computer for 6 months now, but i can’t get myself to work on it. Basically just need to insert some references and look thru some studies. Perhaps the theory is bunk. I did try to find data on kinsey scale ratings vs. number of children, but didnt find anything.

Since it is of not much use to me lying on my hard drive, i will publish it now.


An evolutionary theory of the origin of same-sex sexual acts based on social bonding

Emil Kirkegaard, Department of Linguistics, Aarhus University


Homsexuality in humans and other animals [get some refs from wikipedia] is a mystery [ref to Buss’s textbook]. The mystery goes like this: homosexualiy seems so obviously bad for inclusive fitness that it very strange that evolution has not filtered it out. The reason that it is bad, is that homosexuals do not have children. This is not correct [insert studies with data about sexuality and number of children], and the misleadingly simple terms “homosexual”, “bisexual” and “heterosexual” make it harder. It is better to use a Kinsey scale of sexuality [cites, perhaps grab some from Wiki]. Using such a scale, one would expect that people that score more towards the homosexual end have fewer children. [look for studies about this]. But people with scores toward the low end of the Kinsey scale are here and data from research on people’s ability to detect people that are ‘homosexual’ (popularly called the gaydar) suggests that humans have evolved the ability to pretty reliably detect people that have sexual interest in the same sex as themselves. [cite some of the studies mentioned on Wikipedia].

In this paper we propose an evolutionary explanation of sexual interest in the same sex. This theory is one among many theories that attempt to explain the evolutionary origins of same-sex sex acts. Some of these theories work via kin selection, and are called ‘good uncle’ theories. The idea is that even though a ‘homosexual’ family member may have reduced fitness, he conves fitness indirectly by helping his relatives. Another interesting theory is that same-sex sexual behavior is due to sexual antagonism which is when genes that improve fitness in the one sex, reduce it in the other and but are positive on balance. Such genes can be selected for and a recent study by [mentioned on Wikipedia page] supports this theory. [use Wikipedia for more cites]

The theory

The theory is based on three assumptions:

  1. Having an interest in both sexes is good for fitness, i.e., scoring somewhere between 1-5 on the scale

  2. Sexual preferences follow a normal distribution or a skewed Gaussian distribution that is skewed towards the heterosexual end of the Kinsey scale

  3. Exclusive homosexuality is bad, i.e. scoring 6 on the scale

The reasoning for these hypotheses is as following.

1. Having an interest in both sexes is good for fitness, i.e., scoring somewhere between 1-5 on the scale

The support is based on social bonding betwen same-sex people. The idea is that having sex helps create bonds between two animals, including humans. This idea works for humans and non-human animals alike. It is known from animal sexuality research that males tend to engage in same-sex sex acts for bonding purposes [cites]. Having stronger bonding with members of the same sex is potentially useful for (surviving) warfare and social hierarchy purposes. These things have over evolutionary time been more important for the human male. So, this effect is stronger for males and would thus skew the distribution more towards homosexuality for men more than for women. This is indeed the case. There are more men than women that rate themselves 6 on the scale. [cites and illustrations for each sex].

Testing this hypothesis in industrialized humans seems hard as there is no longer much of a struggle for survival (natural selection is almost completely without force). In fact, we are probably living in the least violent time ever in evolutionary history (Pinker 2011). But it should be possible to test it in the surviving traditional societies spread around the world. One way to do that is to do a longditutional study of the survival rates for people and their Kinsey scale ratings. If the hypothesis is correct, there should be a slight positive effect on survival rates for the people that are more bisexual, especially for men. This effect may not appear if the society is very hostile to same-sex sexual acts. For this reason, one would need a larger sample than one society to disprove the hypothesis. We are not aware of any studies that have done this [look for such studies].

2. Sexual preferences follow a normal distribution or a skewed Gaussian distribution that is skewed towards the heterosexual end of the Kinsey scale

For this theory to work, sexuality has to be either normally distributed or skewed to the one end. If there were more people at the extreme ends of the scale, this theory would not work. But sexuality does follow a skewed Gaussian distribution. [cites and illustration]

3. Exclusive homosexuality is bad, i.e. scoring 6 on the scale

This is the usual mystery. People that score towards the homosexual end of the scale have fewer (non-adopted) children than those that are in the middle or towards the heterosexual end. [need data but i think this is true]

Selection preasures

The selection preasure for bisexuality, i.e., scale 1-5 moves the sexuality average towards the middle area, while the selection against exclusive homosexuality, i.e. scale 6 moves the sexuality average away from 6. If the theory is correct, then these preasures move the sexuality average to some midway between 0 (furtherst away from 6) and 1-5 (whatever is optimal). Without data about how strong the hypothesized extra strength of bonding with same sex persons is worth, there is no way to deduce from this theory where on the scale the optimal point is for bisexuality. Perhaps the occassional same-sex sexual act is strong enough to maximize the effect (this would favor scale 1-2), perhaps more regular or very regular same-sex acts are necessary (this would favor scale 3-5).


We have proposed a theory to explain the origin of homosexual behavior (exclusive or not) in humans and other animals. Some research seems to support it but more decisive empirical tests are necessary, including ones in traditional societies.


Pinker, Steven (2011). The Better Angels of Our Nature: Why Violence Has Declined. Viking Adult.

Is it possible? Yes. In the exact same way that one normally makes an IQ-test, one can do so with OKC.

  1. Handpick a lot of questions that have to do with intelligence.
  2. Mine a huge data set with those questions and people’s answers to them.
  3. Do a factor analysis.
  4. The g-factor shud turn up. If it doesn’t (1) failed.
  5. Calculate how each question+answer set correlates with g, that is, how g-loaded it is.
  6. Use the questions+answers to infer people’s IQs.

Then, after that has been done:

  • Mine some more data from people’s profiles, and look for correlations with IQ.
  • Do some stats.
  • Share the data.

Technically feasible?
Yes. But the OKC staff might block it if one is not careful. Since to be able to search one has to be logged in. But to see the profiles, one does not need to login. But if one views some 10,000 profiles in a day, they might get suspicious and close the profile. One can get around this by doing the search while logged in, and then mining the information without being logged in (perhaps from multiple different IP addresses).

Difficulty in finding questions+answers? Sort of. One shud crawl users questions page, and use one of the four first sorting options – Sorted by magic, He cares about, Answered recently, Answered in ancient times – as these include all the questions that a given user has answered publicly.

Ethical, legal?
Yes and yes. Legally, people have answered these questions publicly, thus knowing that others can read them. That’s the whole idea with answering them publicly as opposed to privately. In both cases they are used for OKC’s matching algorithms.

I don’t see any ethical problems in doing this. Altho i wudn’t try to popularize picture+IQ score combinations.

Endless study possibilities
OKC has a wealth of information about people, not just intelligence which can be inferred. It is truly a gold mine for psychological research. I note that it is also useful for my ongoing study:

This is another of those ideas that ive had independently, and that it turned out that others had thought of before me, by thousands of years in this case. The idea is that longer expressions of language as made out of smaller parts of language, and that the meaning of the whole is determined by the parts and their structure. This is rather close to the formulation used on SEP. Heres the introduction on SEP:


Anything that deserves to be called a language must contain meaningful expressions built up from other meaningful expressions. How are their complexity and meaning related? The traditional view is that the relationship is fairly tight: the meaning of a complex expression is fully determined by its structure and the meanings of its constituents—once we fix what the parts mean and how they are put together we have no more leeway regarding the meaning of the whole. This is the principle of compositionality, a fundamental presupposition of most contemporary work in semantics.

Proponents of compositionality typically emphasize the productivity and systematicity of our linguistic understanding. We can understand a large—perhaps infinitely large—collection of complex expressions the first time we encounter them, and if we understand some complex expressions we tend to understand others that can be obtained by recombining their constituents. Compositionality is supposed to feature in the best explanation of these phenomena. Opponents of compositionality typically point to cases when meanings of larger expressions seem to depend on the intentions of the speaker, on the linguistic environment, or on the setting in which the utterance takes place without their parts displaying a similar dependence. They try to respond to the arguments from productivity and systematicity by insisting that the phenomena are limited, and by suggesting alternative explanations.


SEP goes on to discuss some more formal versions of the general idea:


(C) The meaning of a complex expression is determined by its structure and the meanings of its constituents.



(C′) For every complex expression e in L, the meaning of e in L is determined by the structure of e in L and the meanings of the constituents of e in L.


SEP goes on to disguish between a lot of different versions of this. See the article for details.

The thing i wanted to discuss was the counterexamples offered. I found none of them to be rather compelling. Based mostly on intuition pumps as far as i can tell, and im rather wary of such (cf. Every Thing Must Go, amazon).


Heres SEP’s first example, using chess notation (many other game notations wud also work, e.g. Taifho):


Consider the Algebraic notation for chess.[15] Here are the basics. The rows of the chessboard are represented by the numerals 1, 2, … , 8; the columns are represented by the lower case letters a, b, … , h. The squares are identified by column and row; for example b5 is at the intersection of the second column and the fifth row. Upper case letters represent the pieces: K stands for king, Q for queen, R for rook, B for bishop, and N for knight. Moves are typically represented by a triplet consisting of an upper case letter standing for the piece that makes the move and a sign standing for the square where the piece moves. There are five exceptions to this: (i) moves made by pawns lack the upper case letter from the beginning, (ii) when more than one piece of the same type could reach the same square, the sign for the square of departure is placed immediately in front of the sign for the square of arrival, (iii) when a move results in a capture an x is placed immediately in front of the sign for the square of arrival, (iv) the symbol 0-0 represents castling on the king’s side, (v) the symbol 0-0-0 represents castling on the queen’s side. + stands for check, and ++ for mate. The rest of the notation serves to make commentaries about the moves and is inessential for understanding it.

Someone who understands the Algebraic notation must be able to follow descriptions of particular chess games in it and someone who can do that must be able to tell which move is represented by particular lines within such a description. Nonetheless, it is clear that when someone sees the line Bb5 in the middle of such a description, knowing what B, b, and 5 mean will not be enough to figure out what this move is supposed to be. It must be a move to b5 made by a bishop, but we don’t know which bishop (not even whether it is white or black) and we don’t know which square it is coming from. All this can be determined by following the description of the game from the beginning, assuming that one knows what the initial configurations of figures are on the chessboard, that white moves first, and that afterwards black and white move one after the other. But staring at Bb5 itself will not help.


It is exacly the bold lines i dont accept. Why must one be able to know that from the meaning alone? Knowing the meaning of expressions does not always make it easy to know what a given noun (or NP) refers to. In this case “B” is a noun refering to a bishop, which one? Well, who knows. There are lots of examples of words refering to differnet things (people usually) when used in diffferent contexts. For instance, the word “me” refers to the source of the expression, but when an expression is used by different speakers, then “me” refers to different people, cf. indexicals (SEP and Wiki).


Ofc, my thoughts about are not particularly unique, and SEP mentions the defense that i also thought of:


The second moral is that—given certain assumptions about meaning in chess notation—we can have productive and systematic understanding of representations even if the system itself is not compositional. The assumptions in question are that (i) the description I gave in the first paragraph of this section fully determines what the simple expressions of chess notation mean and also how they can be combined to form complex expressions, and that (ii) the meaning of a line within a chess notation determines a move. One can reject (i) and argue, for example, that the meaning of B in Bb5 contains an indexical component and within the context of a description, it picks out a particular bishop moving from a particular square. One can also reject (ii) and argue, for example, that the meaning of Bb5 is nothing more than the meaning of ‘some bishop moves from somewhere to square b5’—utterances of Bb5 might carry extra information but that is of no concern for the semantics of the notation. Both moves would save compositionality at a price. The first complicates considerably what we have to say about lexical meanings; the second widens the gap between meanings of expressions and meanings of their utterances. Whether saving compositionality is worth either of these costs (or whether there is some other story to be told about our understanding of the Algebraic notation) is by no means clear. For all we know, Algebraic notation might be non-compositional.


I also dont agree that it widens the gap between meanings of expressions and meanings of utterances. It has to do with refering to stuff, not meaning in itself.

4.2.1 Conditionals

Consider the following minimal pair:

(1) Everyone will succeed if he works hard.
(2) No one will succeed if he goofs off.

A good translation of (1) into a first-order language is (1′). But the analogous translation of (2) would yield (2′), which is inadequate. A good translation for (2) would be (2″) but it is unclear why. We might convert ‘¬∃’ to the equivalent ‘∀¬’ but then we must also inexplicably push the negation into the consequent of the embedded conditional.

(1′) ∀x(x works hard → x will succeed)
(2′) ¬∃
x (x goofs off → x will succeed)
(2″) ∀
x (x goofs off → ¬(x will succeed))

This gives rise to a problem for the compositionality of English, since is seems rather plausible that the syntactic structure of (1) and (2) is the same and that ‘if’ contributes some sort of conditional connective—not necessarily a material conditional!—to the meaning of (1). But it seems that it cannot contribute just that to the meaning of (2). More precisely, the interpretation of an embedded conditional clause appears to be sensitive to the nature of the quantifier in the embedding sentence—a violation of compositionality.[16]

One response might be to claim that ‘if’ does not contribute a conditional connective to the meaning of either (1) or (2)—rather, it marks a restriction on the domain of the quantifier, as the paraphrases under (1″) and (2″) suggest:[17]

(1″) Everyone who works hard will succeed.
(2″) No one who goofs off will succeed.

But this simple proposal (however it may be implemented) runs into trouble when it comes to quantifiers like ‘most’. Unlike (3′), (3) says that those students (in the contextually given domain) who succeed if they work hard are most of the students (in the contextually relevant domain):

(3) Most students will succeed if they work hard.
(3′) Most students who work hard will succeed.

The debate whether a good semantic analysis of if-clauses under quantifiers can obey compositionality is lively and open.[18]


Doesnt seem particularly difficult to me. When i look at an “if-then” clause, the first thing i do before formalizing is turning it around so that “if” is first, and i also insert any missing “then”. With their example:


(1) Everyone will succeed if he works hard.
(2) No one will succeed if he goofs off.


this results in:


(1)* If he works hard, then everyone will succeed.
(2)* If he goofs off, then no one will succeed.


Both “everyone” and “no one” express a universal quantifer, ∀. The second one has a negation as well. We can translate this to something like “all”, and “no” to “not”. Then we might get:


(1)** If he works hard, then all will succeed.
(2)** If he goofs off, then all will not succeed.


Then, we move the quantifier to the beginning and insert a pronoun, “he”, to match. Then we get something like:


(1)*** For any person, if he works hard, then he will succeed.
(2)*** For any person, if he goofs off, then he will not succeed.


These are equivalent with SEP’s


(1″) Everyone who works hard will succeed.
(2″) No one who goofs off will succeed.


The difference between (3) and (3′) is interesting, not becus of relevance to my method about (i think), but since it deals with something beyond first-order logic. Quantification logic, i suppose? I did a brief Google and Wiki search, but didnt find something like that i was looking for. I also tried Graham Priest’s Introduction to non-classical logic, also without luck.


So here goes some system i just invented to formalize the sentences:


(3) Most students will succeed if they work hard.
(3′) Most students who work hard will succeed.


Capital greek letters are set variables. # is a function that returns the cardinality a set.


(3)* (∃Γ)(∃Δ)(∀x)(∀y)(Sx↔x∈Γ∧Δ⊆Γ∧#Δ>(#Γ/2)∧(y∈Δ)→(Wy→Uy))


In english: There is a set, gamma, and there is another set, delta, and for any x, and for any y, x is a student iff x is in gamma, and delta is a subset of gamma, and the cardinality of delta is larger than half the cardinality of gamma, and if y is in delta, then (if y works hard, then y will succeed).


Quite complicated in writing, but the idea is not that complicated. It shud be possible to find some simplified writing convention for easier expression of this way of formalizing it.


(3′)* (∃Γ)(∃Δ)(∀x)(∀y)(((Sx∧Wx)↔x∈Γ)∧Δ⊆Γ∧#Δ>(#Γ/2)∧(y∈Δ→Uy))


In english: there is a set, gamma, and there is another set, delta, and for any x, and for any y, (x is a student and x works hard) iff x is in gamma, and delta is a subset of gamma, and the cardinality of delta is larger than half the cardinality of gamma, and if y is in delta, then u will succeed.


To my logician intuition, these are not equivalent, but proving this is left as an exercise to the reader if he can figure out a way to do so in this set theory+predicate logic system (i might try later).


4.2.2 Cross-sentential anaphora

Consider the following minimal pair from Barbara Partee:


(4) I dropped ten marbles and found all but one of them. It is probably under the sofa.

(5) I dropped ten marbles and found nine of them. It is probably under the sofa.


There is a clear difference between (4) and (5)—the first one is unproblematic, the second markedly odd. This difference is plausibly a matter of meaning, and so (4) and (5) cannot be synonyms. Nonetheless, the first sentences are at least truth-conditionally equivalent. If we adopt a conception of meaning where truth-conditional equivalence is sufficient for synonymy, we have an apparent counterexample to compositionality.


I dont accept that premise either. I havent done so since i read Swartz and Bradley years ago. Sentences like


“Canada is north of Mexico”

“Mexico is south of Canada”


are logically equivalent, but are not synonymous. The concept of being north of, and the concept of being south of are not the same, even tho they stand in a kind reverse relation. That is to say, xR1y↔yR2x. Not sure what to call such relations. It’s symmetry+substitition of relations.


Sentences like


“Everything that is round, has a shape.”

“Nothing is not identical to itself.”


are logically equivalent but dont mean the same. And so on, cf. Swartz and Bradley 1979, and SEP on theories of meaning.


Interesting though these cases might be, it is not at all clear that we are faced with a genuine challenge to compositionality, even if we want to stick with the idea that meanings are just truth-conditions. For it is not clear that (5) lacks the normal reading of (4)—on reflection it seems better to say that the reading is available even though it is considerably harder to get. (Contrast this with an example due to—I think—Irene Heim: ‘They got married. She is beautiful.’ This is like (5) because the first sentence lacks an explicit antecedent for the pronoun in the second. Nonetheless, it is clear that the bride is said to be beautiful.) If the difference between (4) and (5) is only this, it is no longer clear that we must accept the idea that they must differ in meaning.


I agree that (4) and (5) mean the same, even if (5) is a rather bad way to express the thing one normally wud express with something like (4).


In their bride example, one can also consider homosexual weddings, where “he” and “she” similarly fails to refer to a specific person out of the two newlywed.

4.2.3 Adjectives

Suppose a Japanese maple leaf, turned brown, has been painted green. Consider someone pointing at this leaf uttering (6):


(6) This leaf is green.


The utterance could be true on one occasion (say, when the speaker is sorting leaves for decoration) and false on another (say, when the speaker is trying to identify the species of tree the leaf belongs to). The meanings of the words are the same on both occasions and so is their syntactic composition. But the meaning of (6) on these two occasions—what (6) says when uttered in these occasions—is different. As Charles Travis, the inventor of this example puts it: “…words may have all the stipulated features while saying something true, but also while saying something false.”[[20]


At least three responses offer themselves. One is to deny the relevant intuition. Perhaps the leaf really is green if it is painted green and (6) is uttered truly in both situations. Nonetheless, we might be sometimes reluctant to make such a true utterance for fear of being misleading. We might be taken to falsely suggest that the leaf is green under the paint or that it is not painted at all.[21] The second option is to point out that the fact that a sentence can say one thing on one occasion and something else on another is not in conflict with its meaning remaining the same. Do we have then a challenge to compositionality of reference, or perhaps to compositionality of content? Not clear, for the reference or content of ‘green’ may also change between the two situations. This could happen, for example, if the lexical representation of this word contains an indexical element.[22] If this seems ad hoc, we can say instead that although (6) can be used to make both true and false assertions, the truth-value of the sentence itself is determined compositionally.[23]


Im going to bite the bullet again, and just say that the sentence means the same on both occasions. What is different is that in different contexts, one might interpret the same sentence to express different propositions. This is not something new as it was already featured before as well, altho this time it is without indexicals. The reason is that altho the sentence means the same, one is guessing at which proposition the utterer meant to express with his sentence. Context helps with that.

4.2.4 Propositional attitudes

Perhaps the most widely known objection to compositionality comes from the observation that even if e and e′ are synonyms, the truth-values of sentences where they occur embedded within the clausal complement of a mental attitude verb may well differ. So, despite the fact that ‘eye-doctor’ and ‘ophthalmologist’ are synonyms (7) may be true and (8) false if Carla is ignorant of this fact:


(7) Carla believes that eye doctors are rich.
(8) Carla believes that ophthalmologists are rich.


So, we have a case of apparent violation of compositionality; cf. Pelletier (1994).

There is a sizable literature on the semantics of propositional attitude reports. Some think that considerations like this show that there are no genuine synonyms in natural languages. If so, compositionality (at least the language-bound version) is of course vacuously true. Some deny the intuition that (7) and (8) may differ in truth-conditions and seek explanations for the contrary appearance in terms of implicature.[24] Some give up the letter of compositionality but still provide recursive semantic clauses.[25] And some preserve compositionality by postulating a hidden indexical associated with ‘believe’.[26]


Im not entirely sure what to do about these propositional attitude reports, but im inclined to bite the bullet. Perhaps i will change my mind after i have read the two SEP articles about the matter.


Idiomatic language

The SEP article really didnt have a proper discussion of idiomatic language use. Say, frases like “dont mention it” which can either mean what it literally (i.e., by composition) means, or its idiomatic meaning: This is used as a response to being thanked, suggesting that the help given was no trouble (same source).

Depending on what one takes “complex expression” to mean. Recall the principle:


(C′) For every complex expression e in L, the meaning of e in L is determined by the structure of e in L and the meanings of the constituents of e in L.


What is a complex expression? Is any given complex expression made up of either complex expressions themselves or simple expressions? Idiomatic expressions really just are expressions whose meaning is not determined by their parts. One might thus actually take them to be simple expressions themselves. If one does, then the composition principle is pretty close to trivially true.


If one does not take idiomatic expressions to be complex expressions or simple expressions, then the principle of composition is trivially false. I dont consider that a huge problem, it generally holds, and explains the things it is required to explain just fine when it isnt universally true.


One can also note that idiomatic expressions can be used as parts of larger expressions. Depending on which way to think about idiomatic expressions, and of constituents, then larger expressions which have idiomatic expressions as parts of them might be trivially non-compositional. This is the case if one takes constituents to mean smallest parts. If one does, then since the idiomatic expressions’ meanings cannot be determined from syntax+smallest parts, then neither can the larger expression. If one on the other hand takes constituents to mean smallest decompositional parts, then idiomatic expressions do not trivially make the larger expressions they are part of non-compositional. Consider the sentence:


“He is pulling your leg”


the sentence is compositional since its meaning is determinable from “he”, “is”, “pulling your leg”, the syntax, and the meaning function.


There is a reason i bring up this detail, and that is that there is another kind of idiomatic use of language that apparently hasnt been mentioned so much in the literature, judging from SEP not mentioning it. It is the use of prepositions. Surely, many prepositions are used in perfectly compositional ways with other words, like in


“the cat is on the mat”


where “on” has the usual meaning of being on top of (something), or being above and resting upon or somesuch (difficult to avoid circular definitions of prepositions).


However, consider the use of “on” in


“he spent all his time on the internet”


clearly “on” does not mean the same as above here, it doesnt seem to mean much, it is a kind of indefinite relationship. Apparently aware of this fact (and becus languages differ in which prepositions are used in such cases), the designer of esperanto added a preposition for any indefinite relation to the language (“je”). Some languages have lots of such idiomatic preposition+noun frases, and they have to be learned by heart exactly the same way as the idiomatic expressions mentioned earlier, exactly becus they are idiomatic expressions.


As an illustration, in danish if one is at an island, one is “på Fyn”, but if one is at the mainland, then one is “i Jylland”. I think such usage of prepositions shud be considered idiomatic.